Publication
In contrast with linear systems, forced oscillations at particular frequencies may result in more than one stable limit cycle in the dynamic response of a nonlinear system. Also known as jump phenomenon, in these frequency regions, a nonlinear system would exhibit various dynamic behaviors critically depending on the initial conditions. The current study investigates the impact of initial conditions on nonlinear oscillations of an acoustically excited electroacoustic viscoelastic membrane. Accordingly, a mathematical model is developed to simulate the nonlinear dynamics of the membrane, and the method of multiple scales is then utilized to solve the governing equation of motion of the system. Frequency response of the system is extracted to examine the effect of system nonlinearity level on jump phenomenon. Various combinations for initial states of the membrane are taken into consideration, and corresponding phase portraits are provided to study the dynamic response of the system in the jump region. Finally, basins of attraction for stable oscillations are mapped in a plane spanned by initial conditions of the system for different excitation frequencies.